Suppose that it is known that the number of items produced in a factory during a week is a random variable with mean 50,
Answers
Answer:
EXPLANATION.
\sf \implies \displaystyle a^{3} (l + m)^{3} - \bigg( \dfrac{al}{3} + \dfrac{2am}{3} \bigg)^{3} - \bigg(\frac{2al}{3} + \dfrac{am}{3} \bigg)^{3}⟹a
3
(l+m)
3
−(
3
al
+
3
2am
)
3
−(
3
2al
+
3
am
)
3
As we know that,
We can write equation as,
\sf \implies \displaystyle a^{3} (l + m)^{3} - \bigg(\frac{a}{3} \bigg)^{3} (l + 2m)^{3} - \bigg(\dfrac{a}{3} \bigg)^{3} (2l + m)^{3}⟹a
3
(l+m)
3
−(
3
a
)
3
(l+2m)
3
−(
3
a
)
3
(2l+m)
3
\sf \implies \displaystyle a^{3} (l + m)^{3} - \bigg(\frac{a}{3} \bigg)^{3} \bigg[ (l + 2m)^{3} + (2l + m)^{3} \bigg]⟹a
3
(l+m)
3
−(
3
a
)
3
[(l+2m)
3
+(2l+m)
3
]
As we know that,
Formula of :
⇒ (x + y)³ = x³ + 3x²y + 3xy² + y³.
Using this formula in the equation, we get.
\sf \implies \displaystyle a^{3} (l + m)^{3} - \bigg(\frac{a}{3} \bigg)^{3} \bigg[ (l^{3} + 6l^{2}m + 12lm^{2} + 8m^{3}) + (8l^{3} + 12l^{2}m + 6lm^{2} + m^{3} ) \bigg]⟹a
3
(l+m)
3
−(
3
a
)
3
[(l
3
+6l
2
m+12lm
2
+8m
3
)+(8l
3
+12l
2
m+6lm
2
+m
3
)]
\sf \implies \displaystyle a^{3} (l + m)^{3} - \bigg(\frac{a}{3} \bigg)^{3} \bigg[ 9l^{3} + 18l^{2}m + 18lm^{2} + 9m^{3} \bigg]⟹a
3
(l+m)
3
−(
3
a
)
3
[9l
3
+18l
2
m+18lm
2
+9m
3
]
\sf \implies \displaystyle a^{3} (l + m)^{3} - \bigg(\frac{a}{3} \bigg)^{3} \times (9)\bigg[ l^{3} + 2l^{2}m + 2lm^{2} + m^{3} \bigg]⟹a
3
(l+m)
3
−(
3
a
)
3
×(9)[l
3
+2l
2
m+2lm
2
+m
3
]
\sf \implies \displaystyle a^{3} (l + m)^{3} - \bigg(\frac{a^{3} }{27} \bigg) \times (9)\bigg[ l^{3} + 2l^{2}m + 2lm^{2} + m^{3} \bigg]⟹a
3
(l+m)
3
−(
27
a
3
)×(9)[l
3
+2l
2
m+2lm
2
+m
3
]
\sf \implies \displaystyle a^{3} (l + m)^{3} - \bigg(\frac{a^{3} }{3} \bigg) \bigg[ l^{3} + 2l^{2}m + 2lm^{2} + m^{3} \bigg]⟹a
3
(l+m)
3
−(
3
a
3
)[l
3
+2l
2
m+2lm
2
+m
3
]
\sf \implies \displaystyle \bigg( \frac{a^{3} }{3} \bigg) \bigg[ 3(l + m)^{3} - (l^{3} + m^{3} + 2l^{2} + 2lm^{2} ) \bigg]⟹(
3
a
3
)[3(l+m)
3
−(l
3
+m
3
+2l
2
+2lm
2
)]
\sf \implies \displaystyle \bigg( \frac{a^{3} }{3} \bigg) \bigg[ 3(l^{3} + m^{3} + 3l^{2}m + 3lm^{2} ) - (l^{3} + m^{3} + 2l^{2} + 2lm^{2} ) \bigg]⟹(
3
a
3
)[3(l
3
+m
3
+3l
2
m+3lm
2
)−(l
3
+m
3
+2l
2
+2lm
2
)]
\sf \implies \displaystyle \bigg( \frac{a^{3} }{3} \bigg) \bigg[ (3l^{3} + 3m^{3} + 9l^{2} m + 9lm^{2}) - (l^{3}+ m^{3} + 2l^{2} + 2lm^{2} ) \bigg]⟹(
3
a
3
)[(3l
3
+3m
3
+9l
2
m+9lm
2
)−(l
3
+m
3
+2l
2
+2lm
2
)]
\sf \implies \displaystyle \bigg( \frac{a^{3} }{3} \bigg) \bigg[ 2l^{3} + 2m^{3} + 7l^{2} m + 7lm^{2} \bigg]⟹(
3
a
3
)[2l
3
+2m
3
+7l
2
m+7lm
2
]
\sf \implies \displaystyle \bigg( \frac{a^{3} }{3} \bigg) \bigg[ (l^{3} + m^{3} + 3l^{2} m + 3lm^{2} ) + (l^{3} + m^{3} + 4l^{2}m + 4lm^{2} ) \bigg]⟹(
3
a
3
)[(l
3
+m
3
+3l
2
m+3lm
2
)+(l
3
+m
3
+4l
2
m+4lm
2
)]
\sf \implies \displaystyle \bigg( \frac{a^{3} }{3} \bigg) \bigg[2 (l + m)^{3} + lm(l + m) \bigg]⟹(
3
a
3
)[2(l+m)
3
+lm(l+m)]
Answer:
Step-by-step explanation:
Suppose that it is known that the number of items produced in a factory during a week is a random variable with mean 5